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# Counting permutations combinations

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### Counting permutations combinations

1. 1. Warm-up What is the probability that you will pick one cardthat is a number 12 out of a regular deck ofplaying cards? What is the probability that you will pick an evennumber out of the numbers 2, 4, 6, 8, 10?
2. 2. Counting PrinciplePermutationsCombinationsAfter today, you will be able tocount outcomes, usepermutations, and usecombinations.
3. 3. Bagel Mania! Bagel Mania offers chicken, tuna, andvegetable sandwiches on plain or onionbagels. How many possible sandwiches arethere?
4. 4. Tree DiagramChicken Tuna VegetablePlain Onion PlainPlain OnionOnion
5. 5. Counting Principle To find the total number of outcomes, multiplyyour options together. EX) 8 different pizza toppings and 3 types ofcrust (stuffed, thick, thin). How many differentcombinations for a one-topping pizza? EX) Four coins are tossed.
6. 6.  How many different ways can you order an icecream if the choices are: What is the probability the ice cream will be in asugar cone?Type of cone Number ofscoopsIce creamflavorToppingsSugar or waffle One or two Chocolate,vanilla, coffeeor pistachioSprinkles,syrup, or none
7. 7. Permutations Permutation- an arrangement or listing inwhich order is important. How many arrangements are possible with a4-swimmer relay? 4 x 3 x 2 x 1 or 4P4 in your calculator How many arrangements are possible with 5swimmers for a 4-swimmer relay? 5 x 4 x 3 x 2 or 5P4 in your calculator
8. 8. Permutations Find P(8,3) P(8,3) means the number of orders of 8 thingstaken 3 at a time.
9. 9. Combinations Combination- arrangements where order is NOTimportant. Examples:
10. 10. Combinations Ex) In gym class Mr. Merrill picked 10students to compete in the 100m dash. Thetop three finishers each received a freet-shirt. How many combinations of winnerscould there be?
11. 11. Permutation OR Combination? Four books in a row 6 CDs from a group of 20 A team of 6 players from 12 Ten people in line to buy tickets
12. 12. Permutations What is 4! 4! Is read as “four factorial” Find 6!